Surface area

The area of the base should be simple, so the problem is the six triangular sides. Each triangle has area , where b = 6 cm is the length of a side of the base, and l is the height of the triangle. Consider the right triangle formed by a line from the center of the base to the center of one of the sides of the base, by the center axis of the pyramid, and the height l of the side in question. Since b=6 cm, the distance from center of base to the side of the base is . Thus by the pythagorean theorem, , and . From here, you can find the area of one of the triangles. Then just multiply by 6 to get the entire lateral area, and add the area of the base for the entire surface area.